SOLUTION: Please tell me how I can solve this problem. Write the standard form of the equation of the parabola with axis of symmetry x=-1, vertex at (-1, 5) and where f(0)= 3. Graph the eq

Algebra ->  Test -> SOLUTION: Please tell me how I can solve this problem. Write the standard form of the equation of the parabola with axis of symmetry x=-1, vertex at (-1, 5) and where f(0)= 3. Graph the eq      Log On


   

Question 738372: Please tell me how I can solve this problem.
Write the standard form of the equation of the parabola with axis of symmetry x=-1, vertex at (-1, 5) and where f(0)= 3. Graph the equation.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the form of the equation is
+f%28x%29+=+ax%5E2+%2B+b%2Ax+%2B+c+
The x-coordinate of the vertex is at
+-b%2F%282a%29+ , so
+-1+=+-b%2F%282a%29+
+-2+=+-b%2Fa+
+b+=+2a+
-----------
So far I have
+f%28x%29+=+ax%5E2+%2B+%282a%29%2Ax+%2B+c+
------------
You are given the point ( -1,5 ), so
+5+=+a%2A%28-1%29%5E2+%2B+2a%2A%28-1%29+%2B+c+
+5+=+a+-+2a+%2B+c+
+c+=+a+%2B+5+
Now I have
+f%28x%29+=+ax%5E2+%2B+%282a%29%2Ax+%2B+a+%2B+5+
Also given the point
(3,0)
+0+=+a%2A3%5E2+%2B+%282a%29%2A3+%2B+a+%2B+5+
+0+=+9a+%2B+6a+%2B+a+%2B+5+
+16a+=+-5+
+a+=+-5%2F16+
and, since
+b+=+2a+
+b+=+-5%2F8+
and
+c+=+a+%2B+5+
+c+=+-5%2F16+%2B+80%2F16+
+c+=+75%2F16+
--------------
The equation is:
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+f%28x%29+=+%28-5%2F16%29%2Ax%5E2+%2B+%28-5%2F8%29%2Ax+%2B+75%2F16+
--------------
check:
Is the vertex at (-1,5) ?
+5+=+%28-5%2F16%29%2A%28-1%29%5E2+%2B+%28-5%2F8%29%2A%28-1%29+%2B+75%2F16+
+5+=+-5%2F16+%2B+10%2F16+%2B+75%2F16+
+5+=+80%2F16+
+5+=+5+
OK
Does it go through (3,0) ?
+0+=+%28-5%2F16%29%2A3%5E2+%2B+%28-5%2F8%29%2A3+%2B+75%2F16+
+0+=+-45%2F16+-+30%2F16+%2B+75%2F16+
+75%2F16+=+75%2F16+
OK